Abstract: A shortfall of the scattering intensity from protons has been observed in liquids (water, benzene, etc.) and solids (metal hydrogen systems, organic polymers, etc.) using neutron Compton scattering (NCS). The conventional NCS data reduction scheme, used to obtain the scattering intensities, is based on the convolution approximation (CA) of the nuclear momentum distribution with the instrument resolution function. This scheme has been severely criticized. It was claimed that it is the way the energy resolution function is incorporated in the CA data processing that leads to an underestimation of the scattering intensity. In the present work, the CA data reduction scheme is compared to a model-free approach newly proposed by Dorner. This new scheme is independent of the form of the momentum distribution and the resolution function. Specifically, the ratios of the scattering cross section densities of H to C are presented for a measurement on a polyethylene (PE) sample. The new data reduction scheme is shown to lead to the same results as for the experimental data published earlier and treated with the CA approximation thus refuting the aforementioned criticisms.